Economics and Finance On any given trading day, the fluctuation, or change, in t

Question

Economics and Finance

On any given trading day, the fluctuation, or change, in the price (in dollars) of JP Morgan Chase stock, listed on the New York Stock Exchange, is between - 2.00 and 2.00. Suppose the change in price is a random variable with the probability density function shown below. Verify that this is a valid probability density function. What is the probability that the stock price increase a by at least dollar 1.00 on a randomly selected day? What is the probability that the change in stock price is between - 1.00 and 1.00? Find a value c such that P(-c lessthanorequalto X lessthanorequalto c) = 0.90.

Explanation / Answer

A) For a probability density function, area under the curve is 1. Here, area under the curve = 2x(1/2) x 2 x (0.375-0.125) + 2x0.125x2

=0.5 + 0.5 = 1

So, this is a valid probability density function.

B) P(stock price increasing by at least 1) = area under the curve between 1 to 2

= (2-1)x0.25 + (1/2)x1x(0.375-0.25)

= 0.25+0.0625 = 0.3125

C) P(stock price is between -1 and 1) = P( stock price is between 0 and 1) x 2

= (0.5-0.3125)x2 = 0.375

D) P(-c <= x <=c) = 0.9

So, P(x between 0 and c) = 0.9/2 = 0.45

So, 0.125c + (1/2)x c x (0.375-0.125)xc/2 = 0.45

0.125 c + 0.0625c2 = 0.45

So, c = 1.86

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.